Fen completed a triathlon race whose total distance is $D$ kilometers. First, she swam a distance of $0.5$ kilometer. Then, she rode a bicycle for $x$ hours at an average speed of $20$ kilometers per hour. Finally, she ran for $0.5$ hour at an average speed of $v$ kilometers per hour. Write an equation that relates $D$, $x$, and $v$.
Let's find the distance Fen crossed in each section of the race. Then we can add all these up to find the total distance. For example, she rode a bicycle for $x$ hours at an average speed of $20$ kilometers per hour, so Fen crossed $20x$ kilometers in the cycling section of the race: $\begin{aligned} &\phantom{=}\left(20\,\dfrac{\text{kilometers}}{\text{hour}}\right)\left(x\,\text{hours}\right) \\\\ &=20x\,\dfrac{\text{kilometers}}{\cancel\text{hour}}\cdot\,\cancel\text{hours} \\\\ &=20x\,\text{kilometers} \end{aligned}$ Similarly, Fen crossed $0.5v$ kilometers in the running section, and we are given she crossed $0.5$ kilometer in the swimming section. The total distance Fen crossed is the sum of the distances of each section: $D=0.5+20x+0.5v$